\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to
A
-sin(6x - 2)
B
-sin(3x2 - 2x)dx
C
(6x - 2) sin(3x2 - 2x)
D
-(6x - 2)sin(3x2 - 2x)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Let \(3x^{2} - 2x = u\)
\(y = \cos u \implies \frac{\mathrm d y}{\mathrm d u} = - \sin u\)
\(\frac{\mathrm d u}{\mathrm d x} = 6x - 2\)
\(\therefore \frac{\mathrm d y}{\mathrm d x} = (6x - 2) . - \sin u\)
= \(- (6x - 2) \sin (3x^{2} - 2x)\)
Source: Myschool Past Questions Archive (Record #30854)